I’ve always found 1 Cor 11:1-16 to be one of the most perplexing parts of the NT since the whole discussion of head-coverings and gender depends on cultural scripts and house church debates that we are not privy to and do not fully understand.
One new article on this front is by Janelle Peters, “Slavery and the Gendered Construction of Worship Veils in 1 Corinthians,” Biblica 101.3 (2020): 431-443 (which you can read at Peters’ academia.edu page). It’s well-written and has a thesis worthy of consideration. She concludes:
Paul’s instructions give the veil to women in addition to restricting it from men. While recent scholarship has contended that Paul only removes honor from the men, I have shown that Paul extends honor to women by allowing all women to veil. The position that Paul takes away honor from men to assign women marriage veils presumes different contexts for male and female veiling occurring at the same event. As Pitta has advanced, this view is not corroborated by the lack of male veiling in many religious contexts in Corinth, including that of the cult of Isis. It also ignores the significant frequency of female headgear in secular and religious roles. Paul is concerned with messengers, outsiders of angelic or human origins, in 1 Cor 11,1-16 in a manner similar to his relativization of glossolalia as an activity that could be incomprehensible to visitors (1 Cor 14,23). However, as in his instruction with glossolalia, church remains a liturgical activity. The ecclesial gathering does not represent a return to ordinary time in public, non-church settings with accompanying lesser expectations for veiling. By having the Corinthian Christians veil according to their gender during their assembly, Paul implies that the Corinthians should identify by their gender instead of by their social class, which would have proscribed the veil from some of them. Paul progresses through his instruction trying to unravel the hierarchies whose formulations he mimics at the beginning of the pericope. Just as men and women are explicitly found to be inter-dependent rather than hierarchically ordered, so free and enslaved persons gain tacit equality.